From 9ebf44d84754adc5b64fcf612c6816c02c80462d Mon Sep 17 00:00:00 2001 From: Benjamin Barenblat Date: Sat, 2 Feb 2019 19:29:23 -0500 Subject: Imported Upstream version 8.9.0 --- plugins/micromega/mfourier.ml | 85 ++++++------------------------------------- 1 file changed, 11 insertions(+), 74 deletions(-) (limited to 'plugins/micromega/mfourier.ml') diff --git a/plugins/micromega/mfourier.ml b/plugins/micromega/mfourier.ml index 37799441..3328abda 100644 --- a/plugins/micromega/mfourier.ml +++ b/plugins/micromega/mfourier.ml @@ -1,13 +1,9 @@ +open Util open Num -module Utils = Mutils open Polynomial open Vect -let map_option = Utils.map_option -let from_option = Utils.from_option - let debug = false -type ('a,'b) lr = Inl of 'a | Inr of 'b let compare_float (p : float) q = Pervasives.compare p q @@ -26,9 +22,6 @@ struct Intervals needs to be explicitly normalised. *) - type who = Left | Right - - (** if then interval [itv] is empty, [norm_itv itv] returns [None] otherwise, it returns [Some itv] *) @@ -37,14 +30,6 @@ struct | Some a , Some b -> if a <=/ b then Some itv else None | _ -> Some itv - (** [opp_itv itv] computes the opposite interval *) - let opp_itv itv = - let (l,r) = itv in - (map_option minus_num r, map_option minus_num l) - - - - (** [inter i1 i2 = None] if the intersection of intervals is empty [inter i1 i2 = Some i] if [i] is the intersection of the intervals [i1] and [i2] *) let inter i1 i2 = @@ -92,10 +77,6 @@ type vector = Vect.t module ISet = Set.Make(Int) - -module PSet = ISet - - module System = Hashtbl.Make(Vect) type proof = @@ -131,14 +112,6 @@ and cstr_info = { (** To be thrown when a system has no solution *) exception SystemContradiction of proof -let hyps prf = - let rec hyps prf acc = - match prf with - | Assum i -> ISet.add i acc - | Elim(_,prf1,prf2) - | And(prf1,prf2) -> hyps prf1 (hyps prf2 acc) in - hyps prf ISet.empty - (** Pretty printing *) let rec pp_proof o prf = @@ -147,26 +120,6 @@ let hyps prf = | Elim(v, prf1,prf2) -> Printf.fprintf o "E(%i,%a,%a)" v pp_proof prf1 pp_proof prf2 | And(prf1,prf2) -> Printf.fprintf o "A(%a,%a)" pp_proof prf1 pp_proof prf2 -let pp_bound o = function - | None -> output_string o "oo" - | Some a -> output_string o (string_of_num a) - -let pp_itv o (l,r) = Printf.fprintf o "(%a,%a)" pp_bound l pp_bound r - - -let pp_iset o s = - output_string o "{" ; - ISet.fold (fun i _ -> Printf.fprintf o "%i " i) s (); - output_string o "}" - -let pp_pset o s = - output_string o "{" ; - PSet.fold (fun i _ -> Printf.fprintf o "%i " i) s (); - output_string o "}" - - -let pp_info o i = pp_itv o i.bound - let pp_cstr o (vect,bnd) = let (l,r) = bnd in (match l with @@ -183,11 +136,6 @@ let pp_system o sys= System.iter (fun vect ibnd -> pp_cstr o (vect,(!ibnd).bound)) sys - - -let pp_split_cstr o (vl,v,c,_) = - Printf.fprintf o "(val x = %s ,%a,%s)" (string_of_num vl) pp_vect v (string_of_num c) - (** [merge_cstr_info] takes: - the intersection of bounds and - the union of proofs @@ -243,8 +191,8 @@ let normalise_cstr vect cinfo = (if n <>/ Int 1 then List.map (fun (x,nx) -> (x,nx // n)) vect else vect), let divn x = x // n in if Int.equal (sign_num n) 1 - then{cinfo with bound = (map_option divn l , map_option divn r) } - else {cinfo with pos = cinfo.neg ; neg = cinfo.pos ; bound = (map_option divn r , map_option divn l)}) + then{cinfo with bound = (Option.map divn l , Option.map divn r) } + else {cinfo with pos = cinfo.neg ; neg = cinfo.pos ; bound = (Option.map divn r , Option.map divn l)}) (** For compatibility, there is an external representation of constraints *) @@ -281,7 +229,7 @@ let load_system l = let sys = System.create 1000 in - let li = Mutils.mapi (fun e i -> (e,i)) l in + let li = List.mapi (fun i e -> (e,i)) l in let vars = List.fold_left (fun vrs (cstr,i) -> match norm_cstr cstr i with @@ -335,9 +283,6 @@ let add (v1,c1) (v2,c2) = (* Printf.printf "add(%a,%s,%a,%s) -> %a\n" pp_vect v1 (string_of_num c1) pp_vect v2 (string_of_num c2) pp_vect (fst res) ;*) res -type tlr = (num * vector * cstr_info) list -type tm = (vector * cstr_info ) list - (** To perform Fourier elimination, constraints are categorised depending on the sign of the variable to eliminate. *) (** [split x vect info (l,m,r)] @@ -381,8 +326,8 @@ let project vr sys = let {neg = n1 ; pos = p1 ; bound = bound1 ; prf = prf1} = info1 and {neg = n2 ; pos = p2 ; bound = bound2 ; prf = prf2} = info2 in - let bnd1 = from_option (fst bound1) - and bnd2 = from_option (fst bound2) in + let bnd1 = Option.get (fst bound1) + and bnd2 = Option.get (fst bound2) in let bound = (bnd1 // v1) +/ (bnd2 // minus_num v2) in let vres,(n,p) = add (vect1,v1) (vect2,minus_num v2) in (vres,{neg = n ; pos = p ; bound = (Some bound, None); prf = Elim(vr,info1.prf,info2.prf)}) in @@ -419,13 +364,13 @@ let project_using_eq vr c vect bound prf (vect',info') = let bndres = let f x = cst +/ x // c2 in let (l,r) = info'.bound in - (map_option f l , map_option f r) in + (Option.map f l , Option.map f r) in (vres,{neg = n ; pos = p ; bound = bndres ; prf = Elim(vr,prf,info'.prf)}) | None -> (vect',info') let elim_var_using_eq vr vect cst prf sys = - let c = from_option (get vr vect) in + let c = Option.get (get vr vect) in let elim_var = project_using_eq vr c vect cst prf in @@ -444,9 +389,7 @@ let elim_var_using_eq vr vect cst prf sys = (** [size sys] computes the number of entries in the system of constraints *) let size sys = System.fold (fun v iref s -> s + (!iref).neg + (!iref).pos) sys 0 -module IMap = Map.Make(Int) - -let pp_map o map = IMap.fold (fun k elt () -> Printf.fprintf o "%i -> %s\n" k (string_of_num elt)) map () +module IMap = CMap.Make(Int) (** [eval_vect map vect] evaluates vector [vect] using the values of [map]. If [map] binds all the variables of [vect], we get @@ -475,8 +418,8 @@ let restrict_bound n sum (itv:interval) = | 0 -> if in_bound itv sum then (None,None) (* redundant *) else failwith "SystemContradiction" - | 1 -> map_option f l , map_option f r - | _ -> map_option f r , map_option f l + | 1 -> Option.map f l , Option.map f r + | _ -> Option.map f r , Option.map f l (** [bound_of_variable map v sys] computes the interval of [v] in @@ -613,12 +556,6 @@ struct |(Some a, Some b) -> a =/ b | _ -> false - let eq_bound bnd c = - match bnd with - |(Some a, Some b) -> a =/ b && c =/ b - | _ -> false - - let rec unroll_until v l = match l with | [] -> (false,[]) -- cgit v1.2.3